NATS don't have stricter requirements
I'm afraid you'll find they do - not, perhaps, for medical certification but for employment.
It's quite straightforward really. The CAA medical is intended to check that you meet the minimum standards and are likely to do so until your next renewal. NATS, at the point of initial certification, are thinking of investing many thousands of pounds in training an individual and wants also to have a reasonable chance of getting a return on that investment. If someone just scrapes through the medical exam, particularly in respect of something that is known to deteriorate over time, the liklihood of that person continuing to pass the medical in years to come is reduced.
So the stricter standards applied by NATS is a business decision rather than a regulatory/licensing decision.